A Switching Memory-Based Event-Trigger Scheme for Synchronization of Lur’e Systems With Actuator Saturation: A Hybrid Lyapunov Method

This article is concerned with the event-triggered synchronization of Lur’e systems subject to actuator saturation. Aiming at reducing control costs, a switching-memory-based event-trigger (SMBET) scheme, which allows a switching between the sleeping interval and the memory-based event-trigger (MBET) interval, is first presented. In consideration of the characteristics of SMBET, a piecewise-defined but continuous looped-functional is newly constructed, under which the requirement of positive definiteness and symmetry on some Lyapunov matrices is dropped within the sleeping interval. Then, a hybrid Lyapunov method (HLM), which bridges the gap between the continuous-time Lyapunov theory (CTLT) and the discrete-time Lyapunov theory (DTLT), is used to make the local stability analysis of the closed-loop system. Meanwhile, using a combination of inequality estimation techniques and the generalized sector condition, two sufficient local synchronization criteria and a codesign algorithm for the controller gain and triggering matrix are developed. Furthermore, two optimization strategies are, respectively, put forward to enlarge the estimated domain of attraction (DoA) and the allowable upper bound of sleeping intervals on the premise of ensuring local synchronization. Finally, a three-neuron neural network and the classical Chua’s circuit are used to carry out some comparison analyses and to display the advantages of the designed SMBET strategy and the constructed HLM, respectively. Also, an application to image encryption is provided to substantiate the feasibility of the obtained local synchronization results.

I. Introduction

With the rapid development of multimedia technology, the master–slave synchronization has become a hot spot owing to its potential applications in the fields of secure communication and image encryption [1], [2], [3]. Many chaotic systems, such as cellular neural networks and classical Chua’s circuits, can be transformed into the form of Lur’e systems. As such, considerable research enthusiasm has been stirred toward the study of synchronization of chaotic Lur’e systems in recent years [4], [5], [6], [7]. For the purpose of achieving synchronization, a series of useful control strategies have been reported in the field of control communities [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28]. Thereinto, networked control methods, owing to the characteristics of highly integrating the cyberspace and the physical space, have drawn remarkable attention. Quantized control [10], [11], sampled-data control [14], [15], [16], and event-triggered control [17], [18], [19], [20], [21] are all classified as networked control methods. In event-triggered control systems, control signals will be generated only when the measured error reaches a certain predefined threshold. As such, in contrast to the time-triggered control (e.g., sampled-data control), the event-triggered control allows a substantial reduction of the network bandwidth. Therefore, it is of great practical and theoretical values to deal with the synchronization problem of chaotic Lur’e systems under event-triggered control, and numerous excellent works have proliferated in [17], [18], [19], and [21].